Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x-6y &= -9 \\ -4x+4y &= 1\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = 4x+1$ Divide both sides by $4$ to isolate $y$ $y = {x + \dfrac{1}{4}}$ Substitute this expression for $y$ in the first equation. $-3x-6({x + \dfrac{1}{4}}) = -9$ $-3x - 6x - \dfrac{3}{2} = -9$ Simplify by combining terms, then solve for $x$ $-9x - \dfrac{3}{2} = -9$ $-9x = -\dfrac{15}{2}$ $x = \dfrac{5}{6}$ Substitute $\dfrac{5}{6}$ for $x$ back into the top equation. $-3( \dfrac{5}{6})-6y = -9$ $-\dfrac{5}{2}-6y = -9$ $-6y = -\dfrac{13}{2}$ $y = \dfrac{13}{12}$ The solution is $\enspace x = \dfrac{5}{6}, \enspace y = \dfrac{13}{12}$.